Question 1134911
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Use "^" to denote exponentiation; and use parentheses where required.  The four answer choices should be<br>
a(n) = 9*4^n
a(n) = 9*(-4)^(n+1)
a(n) = 9*4^(n-1)
a(n) = 9*(-4)^(n-1)<br>
The 2nd and 5th terms are opposite signs, so the common ratio has to be negative; so the first and third answer choices can't be right.<br>
The first term is -36.<br>
The second answer choice gives a(2) = 9*(-4)^3 = 9*-64 = -576.  not right.
The fourth answer choice gives a(2) = 9*(-4)^1 = 9*(-4) = -36.  right.<br>
The problem is more educational if you aren't given answer choices....<br>
The 5th term 2304 is the 2nd term -36, multiplied by the common ratio 3 times:<br>
{{{2304/-36 = -64 = (-4)^3}}}  -->  the common ratio is -4<br>
The 2nd term, -36, is the first term, multiplied by the common ratio once:<br>
{{{-36 = a(1)*(-4)}}}
{{{a(1) = (-36)/(-4) = 9}}}  -->  the first term is 9<br>
The n-th term is the first term, multiplied by the common ration (n-1) times:<br>
{{{a(n) = (9)*(-4)^(n-1)}}}<br>
... which is the 4th answer choice